Analyses of Loggerhead Turtle Nest Monitoring Data
Sarah Hoffman, Biomark Applied Biological Services
Eric Buhle, Biomark Applied Biological Services and Northwest Fisheries Science Center
Justin Perrault, Loggerhead Marinelife Center
Sarah Hirsch, Loggerhead Marinelife Center
2021-06-30
Introduction
Nesting Phenology
Climatology plot
Linear mixed-effects with turtle-level and year-level hierarchical intercepts
stan_lmer
family: gaussian [identity]
formula: doy_encounter ~ (1 | name) + (1 | fyear)
observations: 1813
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Median MAD_SD
(Intercept) 129.8 1.0
Auxiliary parameter(s):
Median MAD_SD
sigma 21.5 0.4
Error terms:
Groups Name Std.Dev.
name (Intercept) 7.3
fyear (Intercept) 3.1
Residual 21.5
Num. levels: name 567, fyear 14
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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanregLinear mixed-effects with turtle-level and year-level hierarchical intercepts and a linear time trend
stan_lmer
family: gaussian [identity]
formula: doy_encounter ~ year_ctr + (1 | name) + (1 | fyear)
observations: 1813
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Median MAD_SD
(Intercept) 129.8 1.1
year_ctr -0.1 0.2
Auxiliary parameter(s):
Median MAD_SD
sigma 21.5 0.4
Error terms:
Groups Name Std.Dev.
name (Intercept) 7.3
fyear (Intercept) 3.3
Residual 21.5
Num. levels: name 567, fyear 14
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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanregLinear mixed-effects with turtle-level and year-level hierarchical intercepts and a linear time trend and weather covariates
stan_lmer
family: gaussian [identity]
formula: doy_encounter ~ year_ctr + humid_std + ws_std + p_std + t_std +
ppt_std + sst_std + (1 | name) + (1 | fyear)
observations: 1813
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Median MAD_SD
(Intercept) 129.7 1.2
year_ctr -0.4 0.6
humid_std 1.1 2.0
ws_std -0.4 2.5
p_std 0.7 1.5
t_std -1.0 2.4
ppt_std 0.5 2.0
sst_std 1.2 1.4
Auxiliary parameter(s):
Median MAD_SD
sigma 21.5 0.4
Error terms:
Groups Name Std.Dev.
name (Intercept) 7.3
fyear (Intercept) 4.6
Residual 21.5
Num. levels: name 567, fyear 14
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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanregHierarchical skew-normal model with turtle-level and year-level intercepts
Family: skew_normal
Links: mu = identity; sigma = identity; alpha = identity
Formula: doy_encounter ~ (1 | name) + (1 | fyear)
Data: turtle (Number of observations: 1813)
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 3000
Group-Level Effects:
~fyear (Number of levels: 14)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 2.83 1.03 1.06 5.18 1.00 871 1158
~name (Number of levels: 567)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 6.45 1.10 4.20 8.40 1.00 465 502
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 129.91 1.06 127.74 131.96 1.00 1267 1584
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 21.94 0.52 20.99 22.97 1.00 1043 1169
alpha -2.06 0.46 -3.03 -1.19 1.00 1681 1893
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Hierarchical skew-normal model with turtle-level intercept and year-level intercept, dispersion and skew
Family: skew_normal
Links: mu = identity; sigma = identity; alpha = identity
Formula: doy_encounter ~ (1 | name) + (1 | fyear)
alpha ~ (1 | fyear)
Data: turtle (Number of observations: 1813)
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 3000
Group-Level Effects:
~fyear (Number of levels: 14)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 2.91 1.04 1.22 5.31 1.00 1029 1410
sd(alpha_Intercept) 2.56 1.19 0.86 5.41 1.00 854 1361
~name (Number of levels: 567)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 5.71 1.04 3.57 7.63 1.01 530 973
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 130.06 1.09 128.00 132.31 1.00 1641 1688
alpha_Intercept -2.68 0.95 -4.78 -1.06 1.00 1508 1647
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 22.23 0.48 21.30 23.18 1.00 1320 2200
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Model selection using LOO
elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
sn_doy1 0.00 0.00 -8203 23.7 120 4.07 16406 47.3
sn_doy0 -4.55 4.09 -8208 23.7 127 3.54 16415 47.5
lmer_doy1 -6.07 7.22 -8209 23.6 138 3.54 16419 47.2
lmer_doy0 -6.54 7.25 -8210 23.6 138 3.55 16419 47.2
lmer_doy2 -7.69 7.38 -8211 23.7 141 3.62 16422 47.3Plot posterior predictive distribution from “full” skew-normal model and compare to data and empirical density for each year
Plot time series of encounter DOY for individual females
Plot posterior distribution of the average encounter DOY in an average year (i.e., setting all other fixed and random effects to zero) for just those females that have been seen in at least 4 years (so their random effects are relatively well identified). The lines are the posterior means. They range from late April to late May, so not a ton of variation, but individual females do seem to have distinct seasonal modes.
Somatic Growth
Hierarchical von Bertalanffy model with turtle-level and year-level \(K\) and global \(L_{\infty}\)
Family: gaussian
Links: mu = identity; sigma = identity
Formula: ccl_max ~ ccl_max0 + (exp(logLinf) - ccl_max0) * (1 - inv_logit(logitK)^dyear)
logitK ~ (1 | name) + (1 | fyear)
logLinf ~ 1
Data: size (Number of observations: 324)
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 3000
Group-Level Effects:
~fyear (Number of levels: 10)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(logitK_Intercept) 0.50 0.16 0.27 0.90 1.00 919 1346
~name (Number of levels: 207)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(logitK_Intercept) 0.55 0.08 0.38 0.72 1.00 431 699
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
logitK_Intercept 3.83 0.24 3.35 4.31 1.00 888 1395
logLinf_Intercept 5.17 0.02 5.14 5.21 1.00 1473 1695
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 1.48 0.08 1.33 1.66 1.00 573 1364
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Plot individual growth trajectories. A few females shrank considerably while others grew much faster than average.
Plot von Bertalanffy growth curves (hyper-mean and female-specific) with data overlay
Proportion of Neophytes
Fit intercept-only binomial GLM
stan_glm
family: binomial [logit]
formula: cbind(neophyte, remigrant) ~ 1
observations: 14
predictors: 1
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Median MAD_SD
(Intercept) -0.58 0.06
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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanregFit binomial GLM with time trend
stan_glm
family: binomial [logit]
formula: cbind(neophyte, remigrant) ~ year_ctr
observations: 14
predictors: 2
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Median MAD_SD
(Intercept) -0.70 0.07
year_ctr -0.12 0.02
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* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanregModel comparison using LOO
elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
glm_neo1 0.0 0.0 -49.1 6.95 3.67 1.11 98.2 13.9
glm_neo0 -26.6 9.5 -75.7 9.03 5.72 1.55 151.4 18.1Plot fitted relationship and PPD along with data and sample confidence intervals
Emergence Success
Zero-inflated binomial models [explain ZIB using example from full model]
Full model fitted to all nests. Binomial component: year-level hierarchical intercept, nest- (observation-) level overdispersion residual, linear time trend, fixed effects of beach, distance to HWL and distance to dune. Zero-inflated component: fixed effects of distance to HWL and distance to dune.
Family: zero_inflated_binomial
Links: mu = logit; zi = logit
Formula: emerged | trials(clutch) ~ year_ctr + beach + dist_hwl_std + dist_dune_std + (1 | fyear) + (1 | nestID)
zi ~ dist_hwl_std + dist_dune_std
Data: nest (Number of observations: 2178)
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 3000
Group-Level Effects:
~fyear (Number of levels: 14)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.64 0.16 0.41 1.02 1.00 484 955
~nestID (Number of levels: 2178)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 1.43 0.03 1.38 1.48 1.00 271 663
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -0.45 0.23 -0.91 0.04 1.01 195 329
zi_Intercept -2.62 0.09 -2.81 -2.44 1.00 2593 2153
year_ctr -0.03 0.04 -0.12 0.05 1.01 425 765
beachJC 0.64 0.16 0.31 0.94 1.01 178 315
beachJB 0.38 0.15 0.05 0.67 1.01 139 189
dist_hwl_std -0.06 0.03 -0.12 0.00 1.01 162 358
dist_dune_std 0.01 0.04 -0.06 0.07 1.02 89 214
zi_dist_hwl_std -0.40 0.11 -0.63 -0.17 1.00 1803 2125
zi_dist_dune_std 0.16 0.08 0.00 0.31 1.00 2899 2511
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Plot probability of nest failure vs. distance from HWL and dune
Plot overall emergence rate vs. distance from HWL and dune
Full model fitted to only nests associated with an encounter. Binomial component: year-level and turtle-level hierarchical intercepts, nest- (observation-) level overdispersion residual, linear time trend, fixed effects of beach, distance to HWL and distance to dune. Zero-inflated component: fixed effects of distance to HWL and distance to dune.
Family: zero_inflated_binomial
Links: mu = logit; zi = logit
Formula: emerged | trials(clutch) ~ year_ctr + beach + dist_hwl_std + dist_dune_std + neophyte + (1 | fyear) + (1 | name) + (1 | nestID)
zi ~ dist_hwl_std + dist_dune_std
Data: subset(nest, beach != "TEQ") (Number of observations: 1428)
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 3000
Group-Level Effects:
~fyear (Number of levels: 14)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.76 0.19 0.48 1.24 1.00 1432 2047
~name (Number of levels: 529)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.51 0.07 0.36 0.64 1.01 225 279
~nestID (Number of levels: 1428)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 1.32 0.04 1.25 1.39 1.00 639 1310
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.06 0.24 -0.42 0.55 1.00 1823 2098
zi_Intercept -2.59 0.11 -2.81 -2.37 1.00 3268 2730
year_ctr -0.05 0.05 -0.16 0.05 1.00 2058 1694
beachJB -0.18 0.12 -0.40 0.05 1.01 1643 2142
dist_hwl_std -0.07 0.04 -0.15 0.01 1.00 1552 2066
dist_dune_std 0.08 0.04 -0.00 0.16 1.00 1555 1840
neophyteremigrant 0.01 0.09 -0.17 0.20 1.00 1664 1938
zi_dist_hwl_std -0.44 0.13 -0.71 -0.19 1.00 3044 2733
zi_dist_dune_std 0.15 0.09 -0.05 0.32 1.00 4879 2306
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).